Maths Year 5/6 Spring Multiplication and Division

In the Spring term, it is likely you will begin to think about more formal SATs preparation for your Year 6s. While this revision will be driven by the specific needs of the children in your class, we hope to help by providing a set of SATs-style questions to accompany each Spring term unit: 'Y6 SATs Practice' is an additional 'Teaching & Group Activities' download.

Each unit still has everything you need to teach a set of related skills and concepts for the whole class: 'Teaching & Group Activities' provides a plan for whole-class teaching; a 'Slide Presentation' brings this teaching to life on the IWB. Fully-differentiated adult-led group activities follow, allowing for small-group personalised learning, where you may deal with children's 'Common Misconceptions'. Fluency can be rehearsed with our 'Practice Sheets', or learning checked with the 'Mastery Activity'. 'Extra support' activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of the associated documents. These bulk downloads are only available to Hamilton Friends and School Subscribers.

Unit 1 Multiples, factors and mental strategies (suggested as 2 days)

Planning and Activities

Day 1 Teaching
Use the ITP Number grid to highlight multiples, look for the lowest common multiple of 2 and 3, 3 and 4, 3 and 6, 6 and 9. Then find the highest common factor of 32, 16 and 24, then 12, 20 and 32.
Group Activities: T with Y6
Y5 -- Derive lowest common multiples and highest common factors. Investigate finding lowest common multiples.
Y6 -- Play games to practise finding common multiples and factors.

Day 2 Teaching
Use mental strategies to multiply 2-digit numbers by 1-digit numbers. Aim to reach given targets.
Further Teaching with Y6
Write the 0.4 times tables. Use this to multiply 2-digit numbers with 1 decimal place by 1-digit numbers. Check the place value of answers is reasonable.
Group Activities: T with Y6
Use the in-depth problem-solving investigation ‘LCM Squares’ as today’s group activity.
Or, use these activities:
Y5 -- Investigation to practise mentally multiplying 2-digit numbers by 1-digit numbers.
Y6 -- Derive the 0.6, then 2.6 times table. Investigation to practise mentally multiplying numbers with 1 decimal place by 1-digit numbers.

You Will Need

  • ITP: Number grid
  • Number cards 2–12
  • Common multiples (see resources)
  • Common factors activity sheet (see resources)
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Double 2-digit numbers

Day 2
Times table bingo

Worksheets

Day 1
Y5: Find common multiples and factors of given numbers.
Y6: Find highest common factor and lowest common multiple of sets of numbers.

Day 2
Y5: Mentally multiply 2-digit numbers by 1-digit numbers. Explain strategies.
Y6: Derive the 0.3 times table then related facts.
Mentally multiply 2-digit numbers with 1 decimal place by 1-digit numbers.

Mastery: Reasoning and Problem-Solving

Y5

  • Is the lowest common multiple of 6 and 4 smaller than the highest common factor of 30 and 45?
    Write common factors of 24 and 48.
    Write common multiples of 3 and 5 up to 60.
    Are any numbers in both sets?
  • True or false?
    There are exactly four 2-digit, common multiples of 3 and 7.
    4 and 5 are common factors of all 2-digit multiples of 10.
    15 is a factor of 100.
  • If 350 ÷ 5 is 70, calculate 350 ÷ 10, 350 ÷ 20 and 350 ÷ 70.
    Now try 350 ÷ 2.5.

Y6

  • Which pair(s) of numbers under 20 have the largest number of common factors? What is the highest common factor?
    Write common multiples of 4 and 6 up to 60. What is the lowest common multiple?
    Use this information to find the lowest common multiple of 8 and 12.
  • Write out the 0.7 times table up to 12 × 0.7. Use this to help you write the 2.7 times table.

Y5 In-depth investigation: LCM Squares
Children use trial and improvement to find the smallest possible total on a square of lowest common multiples.

Y6 In-depth investigation:
Use the Day 2 group activity for Working at ARE/Working at Greater Depth, supporting children working towards ARE.

Extra Support

Y5: Mammoth Multiplications
Using known times tables and place value to multiply, e.g. 4 × 3, 4 × 30, 4 × 300

Y6: Factor Hunt
Finding factors of numbers within times tables

Unit 2 Multiplication (suggested as 3 days)

Planning and Activities

Day 1 Teaching
Model both the grid method and short multiplication to calculate 6 × £5.24. Children choose one of the two methods to calculate the cost of 8 items at £6.79.
Further Teaching with Y6
Children first use grid method to calculate 16 × 258. Then revise and model long multiplication to solve the same calculation.
Group Activities: T with Y6
Y5 -- Use the new method of short multiplication for multiplying amounts of money. Use the grid method for multiplying amounts of money.
Y6 -- Use the digits 1 to 6 to create 3-digit by 2-digit (teen) multiplications. Answer using the grid method, then long multiplication. Estimate and calculate 13, 15, 16, 17 and 18 × 485 using long multiplication.

Day 2 Teaching
Use long multiplication to calculate how many hours there are in a year and in a leap year.
Further Teaching with Y5
Work towards using short multiplication to multiply 3-digit, then 4-digit numbers by 1-digit numbers, discussing the extra column/digit to be multiplied.
Group Activities: T with Y5
Y5 -- Estimate products, then multiply 4-digit numbers by 1-digit numbers. Estimate products, then multiply 4-digit money amounts by 1-digit numbers.
Y6 -- Find how many hours are in a number of days (generated by dice) using long multiplication. Use long multiplication to multiply numbers greater than 20 and move on to numbers greater than 30.

Day 3 Teaching
Estimate before using short multiplication of 4-digit numbers by 1-digit numbers. Discuss top tips for the method.
Further Teaching with Y6
Teach children how to multiply by 30, then use long multiplication to multiply 3-digit numbers by numbers between 30 and 40. In pairs, children calculate a row each, then compare with estimates.
Group Activities: T with Y6
Use the in-depth problem-solving investigation ‘Riveting reversals’ as today’s group activity.
Or, use these activities:
Y5 -- Investigation: find answers to given challenges, using short multiplication of 4-digit by 1-digit numbers.
Y6 -- Find a multiplication of the form □□× □□□ with an answer close to 20,000. Use the grid method. Multiply 33 by 3-digit numbers with identical digits using long multiplication.

You Will Need

  • ‘Find the cost’ (see resources)
  • 0–9 dice
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Times tables

Day 2
Factors and multiples

Day 3
Tables facts and powers of 10

Worksheets

Day 1
Y5: Find the total cost of multiple numbers of items.
Y6: Use grid or long multiplication to multiply 3-digit numbers by numbers between 10 and 20.

Day 2
Y5: Multiply 1-digit by 4-digit numbers using the grid method or short multiplication.
Y6: Use long multiplication to multiply 3-digit numbers by numbers between 20 and 30.

Day 3
Y5: Estimate and solve multiplication calculations; create puzzles.
Y6: Use long multiplication to multiply 3-digit numbers by numbers greater than 30.

Mastery: Reasoning and Problem-Solving

Y5

  • Does 2340 × 8 give the same answer as 4320 × 4? Explain how you are certain that your answer is correct.
  • Choose a strategy for each of these three multiplications. Explain why it is not sensible to use the same method for all three.
    (i) 340 × 5 =
    (ii) 421 × 7 =
    (iii) 350 × 9 =
  • ☐☐☐ × ☐
    Using the digits 3, 5, 6 and 7, how close can you get to 2,000?

Y6

  • Have a go at doing each of these 3 multiplications mentally.
    Explain how you did each one.
    280 × 25 =
    143 × 21 =
    210 × 15 =
    Children could check each using long multiplication or the grid method.
  • Multiply 531 by 16 using long multiplication or the grid method.
    Now double 531 four times to check if this gives the same answer.
  • True or false?
    8 × 572 is the same as 286 × 16.
    15 × 626 is the same as 6260 add 3130.
    24 × 333 is half of 12 × 666.

Y5 In-depth investigation: Riveting reversals
Multiply 4-digit numbers with consecutive digits by a 1-digit number; reverse the 4-digit number and repeat. Find the difference between the two answers.

Y6 In-depth investigation:
Multiply 3-digit numbers with consecutive digits by a 2-digit number; reverse the 3-digit number and repeat. Find the difference between the two answers.

Extra Support

Y5: Multiplication Splits
Using the grid method to multiply 3-digit numbers by 1-digit numbers

Y6: Grid Triplets
Revising using the grid method to multiply 3-digit numbers by 1-digit numbers

Unit 3 Division (suggested as 3 days)

Planning and Activities

Day 1 Teaching
Say that Y5 are going to use a method of division called short division (sometimes nicknamed the ‘bus shelter’ or ‘bus stop’ method). Use a slide presentation or base-10 equipment to model this method of division for 678 ÷ 3. Solve similar divisions.
Group Activities: T with Y5
Y5 -- Solve short division calculations and investigate remainders. Some children use base-10 equipment to help.
Y6 -- Discuss which divisions have an answer more/less than 100 or 1000. Create short divisions with mixed number answers.

Day 2 Teaching
Use the slide presentation, alongside base-10 equipment, to demonstrate using short division to solve 281 ÷ 3. Repeat for 281 ÷ 6 and 281 ÷ 5.
Further Teaching with Y6
Write 632 ÷ 14. Write the multiples of 14 and then use these to solve 632 ÷ 14 using long division. Repeat this process with 532 ÷ 17.
Group Activities: T with Y6
Y5 -- Solve short division calculations and investigate remainders, including examples where the first digit is less than the divisor.
Y6 -- Use step-by-step ‘efficient chunking’ to perform long division. Practise long divisions and then create similar divisions using the same number and different divisors.

Day 3 Teaching
Y5 calculate 742 ÷ 4 and 742 ÷ 8, and compare the answers. Y6 calculate 348 ÷ 24 and 510 ÷ 24 and compare answers.
Group Activities: T with Y5 or Y6 according to assessment on Days 1 and 2
Use the in-depth problem-solving investigation ‘Dozen divisions’ as today’s group activity.
Or, use these activities:
Y5 -- Explore division, expressing remainders as fractions.
Y6 -- Divide by 16 using the step-by-step chunking process; write remainders as fractions and as equivalent decimals for halves/quarters. Explore patterns of answers ending in .25 or .75 when dividing by 16 and attempt to find dividends with answers ending in .5.

You Will Need

  • Base-10 equipment
  • Slide presentation (see resources)
  • 1–9 number cards
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Times tables

Day 2
17 times table

Day 3
Equivalent fractions and decimals

Worksheets

Day 1
Y5: Divide 3-digit by 1-digit numbers, including answers with remainders.
Y6: Divide 3-digit and 4-digit numbers by 1-digit numbers, writing answers as mixed numbers.

Day 2
Y5: Divide 3-digit by 1-digit numbers, including word problems.
Y6: Write multiples and use these to help with long division of 3-digit numbers by 2-digit numbers (answers with remainders).

Day 3
Y5: Divide 3-digit by 1-digit numbers; write remainders as fractions in their simplest form.
Y6: Write multiples and use these to help with long division of 3-digit numbers by 2-digit numbers, writing remainders as decimals and/ or fractions.

Mastery: Reasoning and Problem-Solving

Y5

  • Fill in the missing digits (see download) in this vertical chunking division calculation:
    7 8 3 ÷ 9 = ☐
    Complete the same calculation using short division.
    Which method did you find easier? Explain why.
  • (i) Is the answer to 1539 ÷ 3 treble the answer to 1539 ÷ 9?
    (ii) Now use short division to find an answer to both calculations. Was your answer to (i) correct?

Y6

  • Answer the following:
    558 ÷ 9
    308 ÷ 7
    7302 ÷ 6
    £93.52 ÷ 8
  • Which of the following divisions give an answer which ends 1/4 or .25?
    3750 ÷ 24
    2223 ÷ 18
    7300 ÷ 16
    Write two more calculations in the form  ÷  that also give a remainder of 1/4.

In-depth investigation: Dozen divisions
Y5 Children use short division to divide 3-digit numbers with consecutive digits by 12. They reverse the digits in the 3-digit number and repeat, then find the difference between the two answers. Y6 As Year 5, but children use long division to divide 3-digit numbers by 2-digit numbers less than 30.

Extra Support

Y5: Any Left?
Using chunking to divide, answers between 10 and 20, with remainders

Y6: Any left?
Using chunking to divide (answers less than 100)

Unit 4 4-Digit multiplication and division (suggested as 4 days)

Planning and Activities

Day 1 Teaching
Estimate and then solve 5783 × 7. Write 2341, 5372, 4278, 6143. Divide the class into 4 groups. A child from each group takes a 3–9 digit card. Each group decides which number to multiply by the card number, aiming for an answer close to 20,000.
Group Activities: T with Y5
Y5/Y6 -- Use given digits to create 4-digit by 1-digit multiplications with answers as near to a given target as possible.

Day 2 Teaching
Use both grid method and short multiplication to model finding the cost of 6 hoodies (6 × £25.79) and 7 pairs of jeans (7 × £34.45).
Further Teaching with Y6
A teacher travels 16 miles to and from school for 195 days a year. How far in a year? Estimate then show how to use long multiplication to work out 16 × 195. Check using the grid method. Repeat for 23 miles × 195 days.
Group Activities: T with Y6
Y5 -- Estimate products, then multiply 4-digit money amounts by 1-digit numbers.
Y6 -- Use the context of 24 hours in a day to multiply by 24 to find the number of hours in a year or other 3-digit numbers of days. Use long multiplication to calculate how many days, then hours, children have been alive.

Day 3 Teaching
Use short division to divide 4-digit numbers by 1-digit numbers, using base 10 equipment and/or slide presentation.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘Division remainder patterns’ as today’s group activity.
Or, use these activities:
Y5 -- Explore division, expressing remainders as fractions. Some children will explore division, looking for answers in given ranges.
Y6 -- Use short division in a problem-solving context.

Day 4 Teaching
Discuss estimates and then divide 4-digit numbers of legs by 3 to find how many toy aliens can be made.
Further Teaching with Y6
List multiples of 32 to find how many 32-page comic books can be made using 3-digit then 4-digit numbers of pages.
Group Activities: T with Y6
Y5 -- Explore division, looking for answers in given ranges. Divide 4-digit money amounts by 1-digit numbers.
Y6 -- Choose 3-digit numbers to divide by 18. Estimate answers, then solve problems involving long division by 32, using efficient chunking.

You Will Need

  • 1–9 digit cards
  • Large cards
  • Calendars
  • Slide presentation (see resources)
  • Base-10 equipment
  • ‘Short division’ sheet 1 (see resources)
  • ‘Short division’ sheet 2 (see resources)
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Times tables

Day 2
Factors and multiples

Day 3
Count in 1/4s and 1/8s

Day 4
Multiplication and division facts

Worksheets

Day 1
Y5: Use given digits to make 4-digit by 1-digit multiplications with answers as close to given products as possible.
Y6: Use short multiplication to multiply amounts of money, aiming for answers close to £200.

Day 2
Y5: Estimating and solving multiplication problems with money.
Y6: Use the grid method to multiply 3-digit numbers by 2-digit numbers.
Use long multiplication to multiply 3- and 4-digit numbers by 2-digit numbers.

Day 3
Y5: Divide 4-digit by 1-digit numbers, including word problems.
Y6: Practise using short division then answer word problems requiring decisions about remainders.

Day 4
Y5: Match 4-digit ÷ 1-digit divisions with given answers. Use short division or multiplication to check answers.
Y6: Write multiples of given 2-digit numbers and use these to divide 3- and 4-digit numbers.

Mastery: Reasoning and Problem-Solving

Y5

  • Choose a method to find:
    50 × 70 = ☐
    879 × 3 = ☐
    71 × 16 = ☐
    54 × 23 = ☐
    2307 × 4 = ☐
  • A crate contains 27 boxes of oranges. There are 24 oranges in a box. A supermarket orders 3 crates of oranges. How many oranges is this in total?
  • How many hours are there altogether in November and December?
  • Tom’s baby sister Katie has been alive for 3000 hours. How many days is this?

Y6

  • Complete each multiplication using a different method:
    (i) 4530 × 23
    (ii) 399 × 25
    (iii) 476 × 6
  • Multiply 531 by 32 using long multiplication or the grid method. Now double 531 five times to check if this gives the same answer.
  • Tom multiplies his number by 9 and gets 7074. What was his starting number?
  • If Sally multiplies a number by 12, she gets 9,432. What was her starting number?

In-depth investigation: Division remainder patterns
Children look at patterns of remainders in 4-digit numbers when dividing by numbers 3 to 6. Can they establish a rule?

Extra Support

Y5: Multiplying Choices
Using the grid method to multiply 3-digit numbers by 1-digit numbers

Y6: Monster Multiplications
Using known times tables and place value to multiply, e.g. 6 × 4, 6 × 40, 6 × 400

Aim for 2000
Using the grid method to multiply 3-digit numbers by 1-digit numbers